The sharp affine isoperimetric inequality that bounds the volume of the centroid body of a star body (from below) by the volume of the star body itself is the Busemann-Petty centroid inequality. A decade ago, the Lp analogue of the classical BusemannPetty centroid inequality was proved. Here, the definition of the centroid body is extended to an Orlicz centroid body of a star body, and the corr...

Numerical algorithms are developed for the centroid molecular dynamics (centroid MD) method to calculate dynamical time correlation functions for general many-body quantum systems. Approaches based on the normal mode path integral molecular dynamics and staging path integral Monte Carlo methods are described to carry out a direct calculation of the force on the centroid variables in the centroi...

Some gyrocommutative gyrogroups, also known as Bruck loops or K-loops, admit scalar multiplication, turning themselves into gyrovector spaces. The latter, in turn, form the setting for hyperbolic geometry just as vector spaces form the setting for Euclidean geometry. In classical mechanics the centroid of a triangle in velocity space is the velocity of the center of momentum of three massive ob...

Pseudo-Centroid Clustering replaces the traditional concept of a centroid expressed as a center of gravity with the notion of a pseudo-centroid (or a coordinate free centroid) which has the advantage of applying to clustering problems where points do not have numerical coordinates (or categorical coordinates that are translated into numerical form). Such problems, for which classical centroids ...

This work addresses the problem of detecting local centroid paths, paths within an area of interest on a spatial network that has the highest concentration of activities. The KMR algorithm [1] is used to do clustering on the spatial network, and a new measure of the density of activities on a path, Activity Coverage Rate (ACR), is introduced to locate each such path. We use experiment results t...

In recent years we have seen a tremendous growth in the volume of text documents available on the Internet, digital libraries, news sources, and company-wide intranets. Automatic text categorization, which is the task of assigning text documents to pre-specified classes (topics or themes) of documents, is an important task that can help both in organizing as well as in finding information on th...

The Gibbs Centroid Sampler is a software package designed for locating conserved elements in biopolymer sequences. The Gibbs Centroid Sampler reports a centroid alignment, i.e. an alignment that has the minimum total distance to the set of samples chosen from the a posteriori probability distribution of transcription factor binding-site alignments. In so doing, it garners information from the f...